Theory of Generated Space — Particle-sector closure: a TGP-structured derivation of charged-lepton masses, the Koide relation, and the Cabibbo angle

Preprint and supporting numerical material for the TGP particle-sector closure paper, a companion to the TGP core paper (Zenodo DOI: 10.5281/zenodo.19670324). Starting from the substrate-field framework fixed by the core paper, we derive, from the same soliton ODE: (i) the charged-lepton mass law m_n = c_M · A_tail,n^4, with m_μ/m_e = 206.74 vs PDG 206.768 (0.013%); (ii) the Koide relation K = 2/3 as a theorem of the Brannen ratio B = b/a = √2; (iii) the integer N = 3 generation count from a metric-singularity barrier g0_crit = 2.206 with g0^τ safely inside the well; (iv) the Cabibbo angle λ_C via a Z₃ self-energy subtraction on GL(3,𝔽₂), reducing PDG tension from 4.8σ to 0.75σ. The perturbative coefficient α_3 = π²/128 + P_cos is decomposed, with P_cos = 0.0126159… shown at 40-digit precision to have no relation to any 24-element polylog/Clausen basis at max-coef 10^14; it is promoted to a TGP-named constant. Quark Koide is shown to be RG-invariant under 2-loop QCD γ_m with K_u = 0.8746 and K_d = 0.7398, and the neutrino Brannen-√2 ansatz is falsified by Δm² oscillation data (max K_ν = 0.553 in NO), establishing that Koide K = 2/3 is a charged-lepton signature of the soliton ODE, not a universal law. The repository contains the paper source, compiled PDF, and the numerical folders that are directly cited: particle_sector_closure/, brannen_sqrt2/, why_n3/, mass_scaling_k4/, cabibbo_correction/, and neutrino_msw/.